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In the problem of cache-aided multiuser private information retrieval(MuPIR), a set of $K_{\rm u}$ cache-equipped users wish to privately download aset of messages from $N$ distributed databases each holding a library of $K$messages. The system works in two phases: {\it cache placement (prefetching)phase} in which the users fill up their cache memory, and {\it private deliveryphase} in which the users' demands are revealed and they download an answerfrom each database so that the their desired messages can be recovered whileeach individual database learns nothing about the identities of the requestedmessages. The goal is to design the placement and the private delivery phasessuch that the \emph{load}, which is defined as the total number of downloadedbits normalized by the message size, is minimized given any user memory size.This paper considers the MuPIR problem with two messages, arbitrary number ofusers and databases where uncoded prefetching is assumed, i.e., the usersdirectly copy some bits from the library as their cached contents. We propose anovel MuPIR scheme inspired by the Maddah-Ali and Niesen (MAN) coded cachingscheme. The proposed scheme achieves lower load than any existing schemes,especially the product design (PD), and is shown to be optimal within a factorof $8$ in general and exactly optimal at very high or low memory regime.

A New Design of Cache-aided Multiuser Private Information Retrieval with Uncoded Prefetching